Peter Tatchell is backing a campaign to amend the Public Order Act to stop it being abused for the purposes of frivolous prosecution. Photograph: Linda Nylind for the Guardian

What a pleasure to wake up, not only to find the sun shining on the kitchen again but to hear Peter Tatchell on the radio defending free speech in wise and generous terms worthy of the national treasure which the legendary gay rights activist has gradually become.

What was Tatchell on about? The campaign which has united diehard rivals such as the National Secular Society and the Christian Institute, not to mention loads of MPs and even peers, to amend the 1986 Public Order Act to stop it being abused for the purposes of frivolous prosecution by the coppers.

Reformers want section 5 of the act amended so that the offence of using "insulting words and behaviour" should have the vague and subjective word "insulting" removed while upholding protection against threatening and abusive speech – that is to say, speech which threatens public order.

It may seem arcane, but activists like Tatchell have good grounds for complaint. Campaigners have been arrested for waving placards calling the Church of Scientology a "dangerous cult" – that's putting it mildly – outside the organisation's (whoops, I mean cult's) London HQ. An Oxford student who asked a mounted officer: "Excuse me, do you realise your horse is gay?" was arrested and fined £80 (the case was later abandoned after he refused to pay) for making "offensive homophobic remarks".

Even when such a remark is not a joke – that's J-O-K-E officer – Tatchell was prepared to argue on Radio 4 this morning that the rather more unpleasant "Death Penalty for Fags" posters he has occasionally encountered are "one of the prices we pay for freedom of speech" – offensive but not more.

Well, he should know, having been in the thick of all sorts of campaigning, some of it (trying to arrest Robert Mugabe) quite dangerous. I first met him after he was selected to be Labour's candidate in Bermondsey in 1981, an advocate of direct extra-parliamentary action and a militant gay rights advocate in less tolerant times.

Michael Foot, then struggling as Labour leader, felt obliged to denounce him, though I doubt if his heart was in it. The whole affair struck me as pretty futile. Bermondsey's leftwing activists – part of the surge that took Ken Livingstone (remember him?) into power at County Hall – were being deliberately provocative and insensitive trying to impose an exotic foreigner (Peter is Australian by birth) on what was still a white and very tribally working class Surrey docklands seat.

Tatchell hung on and duly lost the squalidly-fought 1983 byelection to the Liberal, Simon Hughes, who preferred to keep his private life private and has kept the now-much-gentrified constituency ever since. Pretty well everyone came out of the 1983 spat badly, including Hughes and his "The Straight Choice" (geddit?) leaflets. Except that Peter kept going on a huge range of issues and gradually won public respect, even affection, for his pluck and tenacity.

Imperialism, sexual politics, the environment (he joined the Greens), animal rights, there he was again. He even penned a Guardian article urging self-rule for my native Cornwall – pretty daft, but where's the harm in it as long as no one takes much notice.

Tatchell also matured – we all do – so that he was able to make his various cases in more connected ways that widened his appeal. So far as I know he still lives in his small Bermondsey flat, nowadays a youthful 60 but unchanged by years of attention and growing reputation. Good for him and he's right about this one. Sticks and stones, bricks and bottles, may break our bones, but names alone will only hurt feelings – and modern society pays too much lip-service (and tribunal payouts) to feelings, hurt or otherwise.

They also cut both ways. Members of Outrage were held for waving posters against supporters of Hizb ut-Tahrir, a nasty Islamist group. Christian preachers rallying against gays in their usual weary-but-sincere way, get arrested and charged (at least in Workington) for telling passersby it's a sin. It may be unkind, but freedom to express one's views matters more, says Peter Tatchell, in 2012.

Good. And he's far from alone in urging the change on Theresa May who has been struggling to exercise her own right to free speech at the bolshie Police Federation's conference – the lads don't like being reformed and have been pretty successful at resisting attempts by successive governments to raise their game. Two thirds of MPs polled by ComRes agreed with the section 5 reform proposal.

The Home Office has put it out for consultation, a process now over. But the coalition is yet to express its own views. Free speech can be fairly nasty – just look at the way women writers in particular are sometimes abused by the internet's trolling tendency – and always has legitimate limits: you can't shout "Fire!" in a crowded cinema.

But it's always under threat, from the well meaning as well as the malign, and it has constantly to be defended from both.